Math Word Problems Demystified - A Self Teaching Guide

SOLUTION:

GOAL: You are being asked to find two consecutive numbers whose product

is 306.

STRATEGY: Letx¼the first number

andxþ 1 ¼the next number

The equation for the product isx(xþ1)¼306.

IMPLEMENTATION: Solve the equation:

xðxþ 1 Þ¼ 306

x^2 þx¼ 306

x^2 þx
 306 ¼ 306 
 306

x^2 þx
 306 ¼ 0

ðxþ 18 Þðx
 17 Þ¼ 0

xþ 18 ¼ 0 x
 17 ¼ 0

xþ 18 
 18 ¼ 0 
 18 x
 17 þ 17 ¼ 0 þ 17

x¼
 18 x¼ 17

xþ 1 ¼
 18 þ 1 ¼
 17 xþ 1 ¼ 17 þ 1 ¼ 18

Hence the numbers are 17 and 18 or
17 and
18.

EVALUATION: Find the product: 17 18 ¼306, and
 17 (
18)¼306.

EXAMPLE:The sum of two numbers is 12. If the sum of their reciprocals is

3

8 , find the numbers.

234 LESSON 19 Using Quadratic Equations